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General Relativity and Quantum Cosmology

Title:
Casimir effect in free-fall towards a Schwarzschild black hole

Abstract: In this paper we discuss the Casimir effect in a small cavity, freely falling
from spatial infinity in spacetime geometry outside of a Schwarzschild black
hole. Our main goal is to search for possible changes in the vacuum energy, as
well as particle creation inside the falling cavity, with respect to a comoving
observer. Working in the Lema\^itre chart and assuming a cavity size $L$ much
smaller than the Schwarzschild radius ($L/r_g\ll 1$), we solve the Klein-Gordon
equation for a massless scalar field confined within the cavity in the
reference frame of the comoving observer. We follow Schwinger's proper time
approach, evaluating the one-loop effective action for the field in the falling
cavity hence evaluating the corrections to the vacuum energy. We find a small
reduction in the absolute value of Casimir energy as the cavity approaches the
black hole horizon due to the changing spacetime geometry. Since the spacetime
geometry for the cavity changes dynamically, we further find the energy density
of the created particles due to the dynamical Casimir effect. These dynamical
contributions exactly match the deficit to the static Casimir energy. Combined,
the observer measures a net increase in energy within the cavity as she falls.

Comments:

13 pages, 1 figure. This paper is the extended version of the manuscript arXiv: 1807.03968 (short version prepared for a talk given at the 15th Marcel Grossmann Meeting, 1-7 July 2018, Rome, Italy)